期刊
ADVANCES IN DIFFERENCE EQUATIONS
卷 -, 期 -, 页码 -出版社
SPRINGER
DOI: 10.1186/s13662-015-0452-4
关键词
Riccati-Bernoulli sub-ODE method; Backlund transformation; traveling wave solution; solitary wave solution; peaked wave solution
资金
- National Natural Science Foundation of China [11372252, 11372253, 11432010]
- Fundamental Research Funds for the Central Universities [3102014JCQ01035]
The Riccati-Bernoulli sub-ODE method is firstly proposed to construct exact traveling wave solutions, solitary wave solutions, and peaked wave solutions for nonlinear partial differential equations. A Backlund transformation of the Riccati-Bernoulli equation is given. By using a traveling wave transformation and the Riccati-Bernoulli equation, nonlinear partial differential equations can be converted into a set of algebraic equations. Exact solutions of nonlinear partial differential equations can be obtained by solving a set of algebraic equations. By applying the Riccati-Bernoulli sub-ODE method to the Eckhaus equation, the nonlinear fractional Klein-Gordon equation, the generalized Ostrovsky equation, and the generalized Zakharov-Kuznetsov-Burgers equation, traveling solutions, solitary wave solutions, and peaked wave solutions are obtained directly. Applying a Backlund transformation of the Riccati-Bernoulli equation, an infinite sequence of solutions of the above equations is obtained. The proposed method provides a powerful and simple mathematical tool for solving some nonlinear partial differential equations in mathematical physics.
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